The questions as phrased are more about granularity. The task of blackmailing the NPC is broken down into 3 sub tasks: 1 Get over the wall. 2 Get into the office. 3 Find the documents. And the ever important but unmentioned - 4 - Get out of the compound with the documents.
And it can further be broken down into:
A - Get to the base of the wall.
B - Toss a grappling hook and get it to catch on something.
C - Succeed in a climb check.
D - Get down off the wall into the compound.
E - Sneak to the office (you do know which of the 10 buildings in the compound is the office????)
F - Open the locked office door.
G - Search for the documents.
H - Deal with guard that noticed the unlocked office door.....
I - Open the safe(because you failed to find the documents outside the safe)
J - Figure out which of the hundreds of documents are the ones in question.
K - Get out of the compound alive and with the documents.
All of the above are while being stealthy. Possibly complicated if the compound isn't really a bad place and the guards are simple employees.
One can assume that the task of blackmailing the NPC is just one sub task of a larger scale task. Maybe the NPC in question is the one that can grant an audience with the King so the PCs can make the argument about sending troops to the border.
This is what I noticed as well. I don't think "effect or intent" is an accurate description of what's being presented.
To me, the better question is: What part of the game is being played? What you break down into many steps vs what you glomp together is basically how you determine what part of the game gets attention and what's filler used to get from one point to the next.
There are many ways to choose when a roll is needed. Some philosophies break it down into narrative steps; you roll the dice when you want the story to have different possible outcomes. Some philosophies focus more on the game; you roll the dice when you want the option to fail or succeed to be meaningful.
Personally, in actual play I ignore most of that kind of game-theory breakdown and focus more on the time it takes for the group to get through the scene and how much fun people are having. What your group spends a lot of time on is hopefully the part that they enjoy the most, and should therefore be the part that has the most rolls. If your group is getting bored with a scene taking too long, that's when you need to start grouping multiple things into less rolls and getting though it faster. If your group is getting super excited about the details, that's when you start breaking things down into more steps and more rolls.
So, going back to the blackmail example:
If the goal of the game is to play a gritty game of action and adventure, have the players go through every step above. The acts of breaking and entering, and the fear factor of stealthy sneaking are the core of the gameplay. This scene could be an entire session.
If you're playing a social-based spy game where the goal is interact with many factions, play them against each other, and roleplay the interactions, then go with the single "Blackmail" roll. Obviously, this blackmail is only one tiny step in a larger plot of playing A against B. It should only take up a minute or two of game play.